本文主要是建立一可生成 之橢圓餘弦波（Cnoidal waves，Cn波）的二維數值黏性造波水槽，並探討此水槽所生成橢圓餘弦波之傳遞特性。建立數值造波水槽的方法係利用數值方法求解二維非穩態的Navier-Stokes方程式及完整的自由液面邊界條件，而上游邊界條件（即入射波浪）則藉由一置放於數值計算域之直推式造波板依Goring and Raichlen (1980) 的造波理論生成所需的波浪。數值黏性造波水槽所得橢圓餘弦波水位及流體質點速度經與理論解及以線性或Madsen造波理論所得之數值解比較皆相當吻合。在波浪傳遞方面，研究結果發現橢圓餘弦波於傳遞過程中隨著 數變小波列會產生不穩定的現象；而當 數較大時，由於黏性的作用，波高會逐漸衰減，且波列最前緣波也會隨傳遞逐漸演變成週期相當長之長波。

　This study investigates the generation and the propagation of cnoidal waves ( ) in a numerical viscous wave tank. The 2-d unsteady Navier-Stokes equations, the exact free surface boundary conditions and the upstream boundary condition at the wavemaker were solved numerically to develop the two-dimensional numerical wave flume. A piston-type wavemaker was set up in the computational domain to produce the incidents cnoidal waves based on the theory proposed by Goring and Raichlen (1980). The accuracy of the numerical results for the incident wave profiles and the associated velocity profiles of the water particle were verified by comparison with the theoretical solutions. For wave propagation, the numerical results showed that the cnoidal waves with larger Ursell number are more stable than those with smaller Ursell number. However, the front edge of the wave trains with larger Ursell number will evolve gradually into several long waves as waves propagate.

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